Search

We show that the prices of risk for factors that are nonlinear in the market return can be obtained using index option prices. The price of coskewness risk corresponds to the market variance risk premium, and the price of cokurtosis risk corresponds to the market skewness risk premium. Option-based estimates of the prices of risk lead to reasonable values of the associated risk premia. An analysis of factor models with coskewness risk indicates that the new estimates of the price of risk improve the models’ performance compared with regression-based estimates.

We investigate the role of co-skewness in pricing stock returns in the Chinese and U.S. markets. In both markets, co-skewness is priced with a negative premium. The annualized factor-adjust...

Despite half a century of research, we still do not know the best way to model skewness of financial returns. We address this question by comparing the predictive ability and associated portfolio performance of several prominent skewness models in a sample of ten international equity market indices. Models that employ information from the option markets provide the best outcomes overall. We develop an option-based model that accounts for the skewness risk premium. The new model produces the most informative forecasts of future skewness, the lowest prediction errors and the best portfolio performance in most of our tests.

We provide a new methodology to empirically investigate the respective roles of systematic and idiosyncratic skewness in explaining expected stock returns. Using a large number of predictors, we forecast the cross-sectional ranks of systematic and idiosyncratic skewness which are easier to predict than their actual values. Compared to other measures of ex ante systematic skewness, our forecasts create a significant spread in ex post systematic skewness. A predicted systematic skewness risk factor carries a significant risk premium that ranges from 7% to 12% per year and is robust to the inclusion of downside beta, size, value, momentum, profitability, and investment factors. In contrast to systematic skewness, the role of idiosyncratic skewness in pricing stocks is less robust. Finally, we document how the determinants of systematic and idiosyncratic skewness differ.

We use a sample of option prices, and the method of Bakshi, Kapadia and Madan (2003), to estimate the ex ante higher moments of the underlying individual securities’ risk-neutral returns distribution. We find that individual securities’ volatility, skewness and kurtosis are strongly related to subsequent returns. Specifically, we find a negative relation between volatility and returns in the cross-section. We also find a significant relation between skewness and returns, with more negatively (positively) skewed returns associated with subsequent higher (lower) returns, while kurtosis is positively related to subsequent returns. To analyze the extent to which these returns relations represent compensation for risk, we use data on index options and the underlying index to estimate the stochastic discount factor over the 1996-2005 sample period, and allow the stochastic discount factor to include higher moments. We find evidence that, even after controlling for differences in co-moments, individual securities’ skewness matters. However, when we combine information in the risk-neutral distribution and the stochastic discount factor to estimate the implied physical distribution of industry returns, we find little evidence that the distribution of technology stocks was positively skewed during the bubble period–in fact, these stocks have the lowest skew, and the highest estimated Sharpe ratio, of all stocks in our sample.

The cross section of stock returns has substantial exposure to risk captured by higher moments of market returns. We estimate these moments from daily Standard & Poor's 500 index option data. The resulting time series of factors are genuinely conditional and forward-looking. Stocks with high exposure to innovations in implied market skewness exhibit low returns on average. The results are robust to various permutations of the empirical setup. The market skewness risk premium is statistically and economically significant and cannot be explained by other common risk factors such as the market excess return or the size, book-to-market, momentum, and market volatility factors, or by firm characteristics.

The shape of the volatility smirk has significant cross-sectional predictive power for future equity returns. Stocks exhibiting the steepest smirks in their traded options underperform stocks with the least pronounced volatility smirks in their options by 10.9% per year on a risk-adjusted basis. This predictability persists for at least 6 months, and firms with the steepest volatility smirks are those experiencing the worst earnings shocks in the following quarter. The results are consistent with the notion that informed traders with negative news prefer to trade out-of-the-money put options, and that the equity market is slow in incorporating the information embedded in volatility smirks.

We develop a one-period model of investor asset holdings where investors have heterogeneous preference for skewness. Introducing heterogeneous preference for skewness allows the model's investors, in equilibrium, to underdiversify. We find suppport for our model's three key implications using a dataset of 60,000 individual investor accounts. First, we document that the portfolio returns of underdiversified investors are substantially more positively skewed than those of diversified investors. Second, we show that the apparent mean-variance inefficiency of underdiversified investors can be largely explained by the fact that investors sacrifice mean-variance efficiency for higher skewness exposure. Furthermore, contrary to the asset-pricing predictions of models that incorporate return skewness in the context of full diversification, we show that idiosyncratic skewness, and not just coskewness, can impact equilibrium prices. Third, the underdiversification of investors does not appear to be coincidentally related to skewness. Stocks most often selected by underdiversified investors have substantially higher average skewness -- especially idiosyncratic skewness -- than stocks most often selected by diversified investors.

Britten-Jones and Neuberger (2000) derived a model-free implied volatility under the diffusion assumption. In this article, we extend their model-free implied volatility to asset price processes with jumps and develop a simple method for implementing it using observed option prices. In addition, we perform a direct test of the informational efficiency of the option market using the model-free implied volatility. Our results from the Standard & Poor's 500 index (SPX) options suggest that the model-free implied volatility subsumes all information contained in the Black--Scholes (B--S) implied volatility and past realized volatility and is a more efficient forecast for future realized volatility. Copyright 2005, Oxford University Press.

We investigate whether the volatility risk premium is negative by examining the statistical properties of delta-hedged option portfolios (buy the option and hedge with stock). Within a stochastic volatility framework, we demonstrate a correspondence between the sign and magnitude of the volatility risk premium and the mean delta-hedged portfolio returns. Using a sample of S&P 500 index options, we provide empirical tests that have the following general results. First, the delta-hedged strategy underperforms zero. Second, the documented underperformance is less for options away from the money. Third, the underperformance is greater at times of higher volatility. Fourth, the volatility risk premium significantly affects delta-hedged gains, even after accounting for jump fears. Our evidence is supportive of a negative market volatility risk premium. The notion that volatility of equity returns is stochastic has a firm footing in financial economics. However, a less than understood phenomenon is whether volatility risk is compensated, and whether this compensation is higher or lower than the risk-free rate. Is the risk from changes in market volatility positively correlated with the economy-wide pricing kernel process? If so, how does it affect the equity and option markets? Evidence that market volatility risk premium may be nonzero can be motivated by three empirical findings: Purchased options are hedges against significant market declines. This is because increased realized volatility coincides with downward market moves [French, Schwert, and Stambaugh (1987) and Glosten, Jagannathan

This paper investigates nonlinear pricing kernels in which the risk factor is endogenously determined and preferences restrict the definition of the pricing kernel. These kernels potentially generate the empirical performance of nonlinear and multifactor models, while maintaining empirical power and avoiding ad hoc specifications of factors or functional form. Our test results indicate that preferencerestricted nonlinear pricing kernels are both admissible for the cross section of returns and are able to significantly improve upon linear single- and multifactor kernels. Further, the nonlinearities in the pricing kernel drive out the importance of the factors in the linear multi-factor model.

If asset returns have systematic skewness, expected returns should include rewards for accepting this risk. We formalize this intuition with an asset pricing model that incorporates conditional skewness. Our results show that conditional skewness helps explain the cross-sectional variation of expected returns across assets and is significant even when factors based on size and book-to-market are included. Systematic skewness is economically important and commands a risk premium, on average, of 3.60 percent per year. Our results suggest that the momentum effect is related to systematic skewness. The low expected return momentum portfolios have higher skewness than high expected return portfolios.

This paper proposes a methodology for the valuation of contingent securities. In particular, it establishes how the characteristic function (of the future uncertainty) is basis augmenting and spans the payoff universe of most, if not all, derivative assets. In one specific application, from the characteristic function of the state-price density, it is possible to analytically price options on any arbitrary transformation of the underlying uncertainty. By differentiating (or translating) the characteristic function, limitless pricing and/or spanning opportunities can be designed. As made lucid via example contingent claims, by exploiting the unifying spanning concept, the valuation approach affords substantial analytical tractability. The strength and versatility of the methodology is inherent when valuing (1) Average-interest options; (2) Correlation options; and (3) Discretely-monitored knock-out options. For each option-like security, the characteristic function is strikingly simple (although the corresponding density is unmanageable/indeterminate). This article provides the economic foundations for valuing derivative securities.

This article examine the role of emerging market bonds in global investment portfolios. The authors explore the history of these bonds and examine expected returns, risk, and higher moments with data extending though the emerging market crash. The authors find that country risk measures are valuable in explaining expected returns and volatilities in these markets. They also argue that the high expected returns are compensation for large negative skewness risk.

We develop a new method for measuring moment risk premiums. We find that the skew premium accounts for over 40% of the slope in the implied volatility curve in the S&P 500 market. Skew risk is tightly related to variance risk, in the sense that strategies designed to capture the one and hedge out exposure to the other earn an insignificant risk premium. This provides a new testable restriction for asset pricing models trying to capture, in particular, disaster risk premiums. We base our results on a general trading strategy by replicating contracts that swap implied for realized conditional asset moments. The Author 2013. Published by Oxford University Press on behalf of The Society for Financial Studies. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com., Oxford University Press.

This article develops a new method for inferring risk-neutral probabilities (or state-contingent prices) from the simultaneously observed prices of European options. These probabilities are then used to infer a unique fully specified recombining binomial tree that is consistent with these probabilities (and, hence, consistent with all the observed option prices). A simple backwards recursive procedure solves for the entire tree. From the standpoint of the standard binomial option pricing model, which implies a limiting risk-neutral lognormal distribution for the underlying asset, the approach here provides the natural (and probably the simplest) way to generalize to arbitrary ending risk-neutral probability distributions. Copyright 1994 by American Finance Association.

We explore the cross-sectional pricing of volatility risk by decomposing equity market volatility into short- and long-run components. Our finding that prices of risk are negative and significant for both volatility components implies that investors pay for insurance against increases in volatility, even if those increases have little persistence. The short-run component captures market skewness risk, which we interpret as a measure of the tightness of financial constraints. The long-run component relates to business cycle risk. Furthermore, a three-factor pricing model with the market return and the two volatility components compares favorably to benchmark models. WHEN MARKET VOLATILITY IS STOCHASTIC, intertemporal models predict that asset risk premia are not only determined by covariation of returns with the mar ket return, but also by covariation with the state variables that govern market volatility. To study this prediction, we model the log-volatility of the market portfolio as the sum of a short- and a long-run volatility component. This ap proach parsimoniously captures shocks to systematic risk at different horizons. Market volatility is a significant cross-sectional asset pricing factor as shown by Ang et al. (2006).l Their two-factor model with the market return and market volatility reduces pricing errors compared to the capital asset pricing model * Joshua Rosenberg and Tobias Adrian are with the Capital Markets Function of the Research and Statistics Group at the Federal Reserve Bank of New York. We would like to thank Robert Stambaugh (the editor), two anonymous referees, John Campbell, Frank Diebold, Robert Engle, Arturo Estrella, Eric Ghysels, Til Schuermann, Kevin Sheppard, Jiang Wang, and Zhenyu Wang for comments. We also thank seminar participants and discussants at the Federal Reserve Bank of

This article provides several new insights into the economic sources of skewness. First, we document the differential pricing of individual equity options versus the market index, and relate it to variations in return skewness. Second, we show how risk aversion introduces skewness in the risk-neutral density. Third, we derive laws that decompose individual return skewness into a systematic component and an idiosyncratic component. Empirical analysis of OEX options and 30 stocks demonstrates that individual risk-neutral distributions differ from that of the market index by being far less negatively skewed. This paper explains the presence and evolution of risk-neutral skewness over time and in the cross-section of individual stocks.

This paper analyses the validity of the three-moment CAPM model in the Indian context. The study is intended to find out whether co-skewness risk is priced in the Indian capital market. To analyse the validity of the three-moment CAPM model in the Indian context, a time period of around 12 years from January 1999 to June 2010 has been chosen. The sample covers 283 companies comprised in BSE-500 index of Bombay Stock Exchange of India. S&P CNX 500 index has been considered as a proxy for the market portfolio. The empirical results of the study confirm the validity of the three-moment CAPM in the Indian capital market and suggest that in addition to systematic standard deviation risk, co-skewness risk is also priced in the Indian capital market when investors price individual securities. The results of the study further show if co-skewness risk is not incorporated in the CAPM model, the traditional CAPM overestimates the expected market premium by 0.30% per month (3.67% per annum compounded annually).

We present a framework for modeling and estimating dynamics of variance and skewness from time-series data using a maximum likelihood approach assuming that the errors from the mean have a non-central conditional t distribution. We parameterize conditional variance and conditional skewness in an autoregressive framework similar to that of GARCH models and estimate the parameters in a conditional noncentral t distribution. The likelihood function has two time-varying parameters, the degrees of freedom and the noncentrality parameter. We apply this methodology to daily and monthly equity returns data from the U.S., Germany and Japan, concurrently estimating conditional mean, variance and skewness. We find that there is significant conditional skewness. We then use this model to understand how the inclusion of conditional skewness affects some of the well-known stylized facts about conditional variance and the relation between returns and conditional variance. Two important stylized facts about conditional variance we examine are persistence and asymmetry in variance. Persistence refers to the tendency where high conditional variance is followed by high conditional variance. Asymmetry in variance, i.e., the observation that conditional variance depends on the sign of the innovation to the conditional mean has been documented in asymmetric variance models used in Glosten, Jagannathan, and Runkle (1993) and Engle and Ng (1993). We find that the evidence of asymmetric variance is really just conditional skewness. Inclusion of conditional skewness also impacts the persistence in conditional variance. However, we also find that there are significant seasonalities in variance and the results also depend on how the seasonal effects are accommodated in the estimation methodology. We also examine the relation between expected returns and volatility.

We infer conditional swap rate moments model independently from swaption cubes. Conditional volatility and skewness exhibit systematic variation across swap maturities and option expiries (conditional kurtosis less so), with conditional skewness sometimes changing sign. Conditional skewness displays some relation to the level and volatility of swap rates but is most consistently related to the conditional correlation between swap rates and swap rate variances. From realized excess returns on synthetic variance and skewness swap contracts, we infer that variance and (to a lesser extent) skewness risk premia are negative and time varying. For the most part, results hold true in both the USD and EUR markets and in both precrisis and crisis subsamples. We design and estimate a dynamic term structure model that captures much of the dynamics of conditional swap rate moments.